where \(H=U+PV\)  is the enthalpy (\(U\)  is the internal energy of the system), and
\(G_0\)  is the Gibbs free energy at \(T=T_0\) . Since the integrand in the first term
on the r.h.s. diverges like \(1/T^{\prime }\)  for classical statistics, direct integration
from \(T_0=0\)  is not possible. Instead, we here calculated \(G_0\)  at
a low temperature \(T_0=25\)  K using the quasi-harmonic approximation (QHA). Within
the QHA, the Helmholtz free energy \(F\)  of the crystal is computed as a function
of temperature \(T\)  and volume \(V\)  via the standard harmonic approximation, while
the Gibbs free energy is found by minimizing \(F(V,T)+PV\)  for a given temperature
and pressure [1]}. Thus, the anharmonic effects are taken into account
only via the volume dependence of the vibrational frequencies. To be compatible
with the classical MD simulations, we computed the harmonic free energies using
classical Maxwell-Boltzmann statistics. We evaluated the integral in
Eq. (REF ) over a path of constant (ambient) pressure for both
monoclinic and tetragonal ZrO\(_2\)  by performing additional MD simulations at
temperatures ranging from 25 K to 1700 K, sampling each trajectory for 300 ps.
The integration paths are continuous, since the tetragonal phase is trapped in
a local minimum and does not transform into the monoclinic one during our MD
simulations (compare Fig. REF a), while the monoclinic phase
remains stable for sufficient time up to 200 K above the transition temperature.
